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Classical monatomic ideal-gas internal energy

Only translational degrees of freedom contribute in this classical ideal-gas model.

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Method and conditions

Only translational degrees of freedom contribute in this classical ideal-gas model.

U = (3/2)nRT

Worked examples

Using R=8.314 J/(mol·K), calculate the internal energy of 9 mol of a classical monatomic ideal gas at 630 K. Round the final result to 4 decimal places if needed. Answer in J.

Three quadratic translational terms contribute RT/2 each per mole. Therefore U=(3/2)(9)R(630).

70710.57 J

Using R=8.314 J/(mol·K), calculate the internal energy of 14 mol of a classical monatomic ideal gas at 410 K. Round the final result to 4 decimal places if needed. Answer in J.

Three quadratic translational terms contribute RT/2 each per mole. Therefore U=(3/2)(14)R(410).

71583.54 J

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  1. Using R=8.314 J/(mol·K), calculate the internal energy of 10 mol of a classical monatomic ideal gas at 730 K. Round the final result to 4 decimal places if needed. Answer in J.

  2. Using R=8.314 J/(mol·K), calculate the internal energy of 1 mol of a classical monatomic ideal gas at 330 K. Round the final result to 4 decimal places if needed. Answer in J.

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Answers and marking notes
  1. 91038.3 J

    Three quadratic translational terms contribute RT/2 each per mole. Therefore U=(3/2)(10)R(730).

  2. 4115.43 J

    Three quadratic translational terms contribute RT/2 each per mole. Therefore U=(3/2)(1)R(330).

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